高层钢筋混凝土框架核心筒结构震后损伤评估方法研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
随着经济的发展,城市化进程的加快,高层建筑所占比例越来越大,地震发生后对高层建筑的损伤评估也显得更加重要。本文从构件尺度、楼层尺度和结构整体尺度对高层钢筋混凝土结构地震损伤评估方法进行了研究。
     1.本文提出了一种基于楼层加速度监测数据小波包能量分析的高层结构震后损伤模糊评价方法。该方法基于小波变换对结构响应信号变化信息敏感的特点,通过实测楼层加速度信号的小波包分解,获得频带能量变化率指标,然后根据能量变化率与实际损伤的关系对损伤程度进行划分,求得能量变化率指标对不同损伤阶段的模糊评判隶属度,最后利用模糊综合评价方法对楼层和结构整体进行损伤程度评分。利用该方法对一实际工程的振动台模型试验进行损伤评估,所得到的损伤评估结果与实际观察损伤情况基本一致。
     2.由于数值计算方法在非线性阶段所采用的分析模型的不准确性,造成大震下结构有限元模型计算结果与实际情况可能存在较大偏差。本文提出基于楼层位移修正的高层框架核心筒结构损伤评估方法,利用实测楼层位移对结构有限元模型楼层计算位移进行修正,并对楼层子结构等效线性刚度模型施加修正后的最大层间位移,计算震后损伤状态的刚度下降情况,从而得到楼层尺度的损伤评估结果。在此基础上经加权组合,也可得到整体结构损伤评价结果。分析发现,位移修正系数随结构塑性发展程度的不同而产生相应的变化,而利用剪重比变化率为变量表达位移修正系数与塑性发展的关系较为合理。
     3.上述小波包能量模糊损伤评估方法和基于位移修正的损伤评估方法均是基于位移信息,从楼层尺度进行损伤评估的。本文通过模型二振动台试验的模型设计和试验工作,对上述两种方法的推广性进行验证。将小波包能量分析模糊评价方法的流程及由模型一总结出的计算参数用于模型二的损伤评估,其结果同样有效,说明利用该方法可以对类似的高层框架核心筒结构地震后的损伤程度进行有效的量化评估。根据基于位移修正的损伤评价方法中利用模型一总结出的以剪重比变化率为变量的位移修正系数计算公式,由模型二的有限元分析结果直接求得位移修正系数,并与由振动台试验得到的位移修正系数相对比,二者之间的偏差在可接受范围之内。说明对于类似形式的高层框架核心筒结构,即使没有安装变形监测系统,也可直接利用有限元分析取得的剪重比变化率求得位移修正系数,并进行损伤评估。
     4.为实现结构震后损伤评估最终落实到构件层次上,本文从建立有限元模型出发,分析各类构件损伤的特点和分布,提出基于损伤分布系数的构件分类损伤评价方法。该方法根据不同类构件的损伤特点采用相应的损伤计算方法得到各类构件的层损伤值,并从能量的角度出发,研究各类构件震后的损伤分布模式,从而可以由事先建立的有限元计算模型和实际地震动输入,快速得到各类构件的具体损伤分布情况。并根据构件类别的不同得到各自的损伤权重系数,通过各类构件的总体损伤结果加权计算,对结构整体损伤进行评估。该方法的特点是能够得到构件尺度的损伤评估结果,而且适用于未安装变形监测系统的结构。通过模型一的数值模拟结果和试验现象的对比验证,说明该方法是有效的。
     本文提出的三种高层钢筋混凝土框架核心筒结构地震损伤评价方法,从不同角度、不同尺度对结构进行损伤评估。经验证,这些方法都是有效的,在工程实际中可以根据不同的实际情况进行选择,也可利用几种方法所得结果相互印证。
As the development of the economic and the quicker pace of the urbanization, the proportion of the high-rise buildings has become larger and larger. Therefore the damage evaluation for high-rise buildings after the earthquakes becomes even more important. This paper is focus on the study of seismic damage evaluation methods for high-rise reinforced concrete structure on different levels of member scale, storey scale and overall structure scale.
     1. In this paper, a method of seismic damage fuzzy evaluation for high-rise buildings is proposed, based on the research on wavelet packets of acceleration data measured in storeys. Considering the sensitive of Wavelet Transform to the changes in signals of structural responses, in the proposed method, the signals of acceleration, which are measured in storeys, are processed by wavelet decomposition to obtain the rate indicators of energy changes in frequency band. After that, the indicators are partitioned by the relation between the rate of energy changes and the real damage, to obtain the membership degree of fuzzy evaluation in different damage states. Then the storeys and overall structure are graded on damage by fuzzy comprehensive evaluation method. Using the proposed method, the damage evaluation is applied on the shaking table model test for the practical project-1. The proposed method provides good agreement with the test results. The parameters needed in the proposed method are obtained through the model test.
     2. Because of the uncertainty in the non-linear constitutive model of materials, which is used in calculation, the results of finite-element analysis of structure under strong earthquakes are probably rather different from the reality. Best on correcting the storey displacements, a damage evaluation method for high-rise frame-core tube structures is proposed in this paper. The storey displacements calculated by finite element analysis are corrected by the measured displacements. The maximum corrected inner-storey displacement is applied on the equivalent linear-stiffness model of sub-structure of storey. Then by calculating the stiffness reduction, the results of damage evaluation on member scale are obtained. The results on overall scale are obtained by weighted combination of the results on member scale. The research shows that the correction coefficient of displacement changes correspondingly with different plastic development state of the structure. A correction coefficient with the rate of shear-weight ratio as variable shows rather reasonable relationship with the plastic development.
     3. The methods of damage fuzzy evaluation based on wavelet packet energy and damage evaluation based on displacement correction are both depend on the information of displacements, and also both on the storey scale. In this paper, the universality of the both methods are verified through the modeling and shaking table test of practical project-2. On the basis of the damage evaluation methods, which are based on displacement correction, when applying the procedures of fuzzy evaluation based on wavelet packet energy and the displacement correction expression with the rate of shear-weight ratio as variable, in which the calculating parameters are obtained from the practical project-1, to the practical project-2, the displacement correction coefficients obtained by finite element method are acceptable compared with the coefficients measured in the table shaking test. Therefore even without the monitoring system for displacement measurement, the displacement correction coefficient can be obtained by finite element method and then used in damage evaluation.
     4. The two methods mentioned above are both on storey scale. However, the same storey damage can be related to different types of member damage; therefore solely evaluation on storey scale is not enough. To solve this problem, in this paper, a damage evaluation method on member scale, which is based on the coefficient of damage distribution, is proposed, through the finite element analysis on the damage distribution of all kinds of memebers. In the proposed method, the storey damage coefficients of different members are obtained by each relevant calculating method, according to their own characteristics of damage. Then the pattern of damage distribution after earthquakes is studied from the energy point of view. Therefore the information of damage distribution of different members is obtained quickly by the existed finite element model and the practical seismic motion input. Also the weight coefficients of their own damage are obtained by weighted computation of different kinds of members’total damages, to evaluate the damage of overall structure. The trait of the proposed method is that it can obtain the damage evaluation results on member scale and it is suitable for the structures without deformation monitoring system. The comparison between the test and the results obtained by numerical modeling of the practical project-1 shows that the proposed method is effective.
     Three methods of seismic damage evaluation for high-rise frame-core tube structure are proposed, to evaluate the damage of structure on different aspects and scales. The proposed methods are verified to be effective. In practical engineering, the proposed methods can be chosen depending on the actual situations, and also the results obtained by three methods can be verified by each other.
引文
[1]祁德庆,李帅,王剑平.海洋平台损伤诊断及非线性动力响应的应用.结构工程师,2008,24(1):41-44
    [2] Vandiver J K.Detection of Structural Failure on Fixed Platform by Measurement of Dynamic Response.Proc.of the 7th Annual Offshore Technology Conference,1975,243~252
    [3] Vandiver J K.Detection of Structural Fai lure on Fixed Platform by Measurement of Dynamic Response.Journal of Petroleum Technology,1977,305~310
    [4] Duggan D M,Wallace E R,Caldwell S R. Measured and Predicted Vibrational Behavior of Gulf of Mexico Platform.Proc.of the 12th Annual Offshore Technology Conference,1980,92~100
    [5] Salane H J,Baldwin J W,Duflield R C.Dynamics Approach for Monitoring Bridge Deterioration.Transportation Research Record,1981,832:21
    [6] Housner G. W., Bergman L. A., et al. Structural Control: Past, Present and Future. Journal of Engineering Mechanics,1997, Vol. 123(9): 897-971
    [7] Turner J D, Pretlove A J. A Study of the Spectrum of Traffic-Induced Bridge Vibration. Journal of Sound and Vibration,1988,122:31~42
    [8] Biswas.M.A.K.Pandey and M.M.Samman.Diagnostic Experimental Spectral Modal Analysis of a Highway Bridge.Modal Analysis:The International Journal of Analytical and Experimental Modal Analysis, 1990.5:33~42
    [9] Alampalli.S.G.Fu.and E.W.Dillon.On the Use of Measured Vibration for Detecting Bridge Damage.Proc.Fourth International Bridge Engineering Conference,1995,125~137
    [10]王柏生,倪一清,高赞明.青马大桥桥板结构损伤位置识别的数值模拟.土木工程学报,2001,34(3):67~73
    [11]瞿伟廉,滕军,项海帆等.风力作用下深圳市市民中心屋顶网架结构的智能健康监测.建筑结构学报,2006,27(1):1-8
    [12]翟伟廉,陈超.深圳市民中心屋顶网架结构支撑钢牛腿瞬时应力场的识别.地震工程与工程振动,2002,22(4):41-46
    [13]李功标,翟伟廉.大型屋顶网壳结构稳定性分析及实时评估策略.武汉科技大学学报(自然科学版),2007,30(4):416-419
    [14]滕军、朱焰煌等.基于复Morlet小波变换的大跨空间结构模态参数识别研究.振动与冲击,2009,28(8),25-29
    [15]钱稼茹,纪晓东,张微敬等.国家游泳中心子结构模型损伤识别试验研究.中国科学(E辑:技术科学),2007,37(05):621~627
    [16]李国强,郝坤超,陆烨.弯剪型悬臂结构损伤识别的柔度法.地震工程与工程振动,1999,19(1):31-37
    [17] Hideaki Iwaki, Keiji Shiba, and Nobuo Takeda. Structural health monitoring system using FBC-based sensor for a damage tolerant building. Smart structure and materials: smart systems and nondestructive evaluation for civil infrastructures, Proceeding of SPIE, San Diego, 2003,5057-49
    [18] Hideaki Iwaki, Hiroshi Yamakawa and Akira Mita. Health monitoring system using FBG-based sensors for a 12-story building with column dampers, Smart structures and materials: smart systems for bridge, structures and highway. Proceeding of SPIE, Newport Beach, 2001,4330-56
    [19]顾远生,李春祥,刘畅,基于希尔伯特-黄变换的超高层建筑模态参数识别,建筑科学,2009,25(3):44-48
    [20] Y.Q. Ni, X.T. Zhou,J.M. Ko. Experimental Investigation of Seismic Damage Identification Using PCA-compressed Frequency Response Functions and Neural Networks.Journal of Sound and Vibration,2006,290,242-263
    [21]张德文、魏阜旋[美].模型修正与破损诊断.北京:科学出版社,1999
    [22] Lifshitz J M,Rotem A. Determinat ion of Reinforcement Unbonding of Composites by a Vibration Technique.Journal of Composite Material S,1969,3:412~423
    [23] P.Cawley,R.D.Adams.The location of Damage in Strueture from Measurements of Natural Frequeneies.Journal of Strain Analysis, 1979.14(2):49~57
    [24] R. J. Allemany and D. L. Brown. A Correlation Coefficient for Modal Vector Analysis. Proc. of the 1st IMAC,1982,110-116
    [25] N. A. J. Lieven and D. J. Ewins. Spatial Correlation of Mode Shape. The Coordinate Modal Assurance Criterion (COMAC) Proc. of the 6th IMAC,1988,690-695
    [26] Pandey, A. K., Biswas, and M. M. Samman. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 1991,145(2):321-332
    [27] Abdo, M A-B and Hori M. A numerical study of structural damage detectionusing changes in the rotation of mode shapes. Journal of sound and vibration, 2002, 251(2):227-239
    [28] O. S. Salawu and C. Williams. Damage Location Using Vibration Mode Shapes. Proc. of the 12th IMAC, 1994,933-939
    [29] A. K. Pendey and M. Biswas. Experimental Verification of Flexibility Difference Method for Locating Damage in Structures. Journal of Sound and Vibration, 1995, 184(2)
    [30] Schulz Z M , Naser A S. Locating structural damage using frequency response functions [ J ] . Journal of Intelligent Material Systems and Structures, 1998, 9:899-905.
    [31] J. C. Chen and J. A. Garba. On-orbit damage assessment for large space structures.AIAA Journal,1988,26(9):1098-1126
    [32] Stubbs. N. and J-T. Kim. Field Verification of a Nondestructive Damage Localization and Severity Estimation Algorithm , Texas A&M Univ. report prepared for New Mexico State Univ., 1994
    [33]赵玲,李爱群,缪长青,汪永兰.大跨斜拉桥的拉索损伤识别.桥梁建设,2004(5):19-22
    [34]刘嫦娟,孙宗光,牛振龙.悬索桥损伤指标的适用性分析.建材技术与应用,2007(1):1-3
    [35]孙宗光,高赞明,倪一清,丁皓江.斜拉桥桥面结构损伤位置识别的指标比较.工程力学,2003,20(1):27-31
    [36] Hua-Peng Chen, N. Bicanic. Inverse damage prediction in structures using nonlinear dynamic perturbation theory. Comput Mech (2006) 37: 455–467
    [37]尹涛,余岭,朱宏平.一种基于模型修正的结构损伤识别方法.振动与冲击,2007,26(6):59-66
    [38] Xiaomo Jiang & Hojjat Adeli. Dynamic Wavelet Neural Network for Nonlinear Identification of High-rise Buildings.Computer-Aided Civil and Infrastructure Engineering,2005,20,316–330
    [39]柯朝辉.基于神经网络的大型悬索桥单损伤识别方法.公路与汽运,2007(3):140-141
    [40]何浩祥,闫维明,王卓.基于子结构和遗传神经网络的递推模型修正方法.工程力学,2008,25(4):99-105
    [41] Ricles J.M., Kosmatka J. B. Damage detection in elastic structures using vibratory residual forces and weighted sensitivity.AIAA J. 1992, 30(9): 2310-2316
    [42] Fang, Sheng-En, Perera, Ricardo, De Roeck, Guido.Damage identification ofa reinforced concrete frame by finite element model updating using damage parameterization.Journal of Sound & Vibration,2008.6, Vol. 313
    [43] Liu P.L. Identification and damage assessment of trusses using modal data. J. Struct. Engrg, ASCE,1995,121(4):599-608
    [44] Ka-Veng Yuen and Lambros S. Katafygiotis. Bayesian Modal Updating using Complete Input and Incomplete Response Noisy Measurements. ASCE,2002,128:3(340)
    [45] Ka-Veng Yuen, Beck, James L., Katafygiotis, Lambros S. Unified Probabilistic Approach for Model Updating and Damage Detection. Journal of Applied Mechanics; Jul2006, Vol. 73 Issue 4, p555-564
    [46] Ka-Veng Yuen. Substructure Identification and Health Monitoring Using Noisy Response Measurements Only. Computer-Aided Civil and Infrastructure Engineering 21 (2006) 280–291
    [47]陈华斌,任伟新.基于响应面的结构有限元模型修正.第十五届全国结构工程学术会议论文集第1册,2006,
    [48]徐军,郑颖人.响应面重构的若干方法研究及其在可靠度分析中的应用.计算力学学报,2002,19(2):217-221
    [49]费庆国,李爱群,张令弥.基于神经网络的非线性结构有限元模型修正研究.宇航学报,2005,26(3):267-281
    [50] Annicchiarico, W. Cerrolaza, M. Identification of the dynamical properties of structures using free vibration data and distributed genetic algorithms. Engineering Optimization; 2007, 39(8):969-980
    [51]邹大力,屈福政,孙铁兵.基于混合遗传算法的子结构损伤识别.农业机械学报,2005,36(5):121-124
    [52]刘涛,李爱群,丁幼亮,王浩.大跨悬索桥损伤预警方法.特种结构,2005,22(3):83-85
    [53]刘涛,李爱群,丁幼亮.基于小波包能量谱的大跨斜拉桥拉索损伤预警方法.东南大学学报(自然科学版),2007,37(2):270-274
    [54]王素华,张伟林.斜拉桥斜索损伤分析中的小波变换研究.安徽建筑工业学院学报(自然科学版),2004,12(3):13-17
    [55]王超,任伟新,黄天立.基于小波的非线性结构系统识别.振动与冲击,2009,28(3):10-13
    [56]任伟新,韩建刚,孙增寿.小波分析在土木工程结构中的应用.中国铁道出版社,2006年
    [57] Staszewski W. J. Structural and mechanical damage detection using wavelets. Shock and Vibration Digest, 1998,30(6):457-472
    [58] Sun Z.,Chang C. C. Strutural damage assessment based on wavelet packet transform. J. Struct. Engrg, ASCE,2002,128(10):1354-1361
    [59] Sun Z., Chang C.C. Statistical wavelet-based method for structural health monitoring. J.Struct. Engrg, ASCE,2004,130(7):1055-1062
    [60] Hera A. Hou Z. Application of wavelet approach for ASCE structural health monitoring benchmark studies. J. Engrg. Mech., ASCE, 2004, 130(1):96-104
    [61] Reda Taha M.M., Lucero J. Damage identification for structural health monitoring using fuzzy pattern recognition. Engineering Structures. 2005, 27(12):1774-1783
    [62]常志巍.基于HHT的地震作用下的结构损伤识别.浙江大学硕士学位论文. 2008
    [63]潘新颖,蒋济同.单自由度结构系统损伤诊断的EMD方法.青岛建筑工程学院学报. 2002,23(1)
    [64]王自平,骆英一,顾建祖,刘红光.基于HHT的钢筋混凝土结构损伤检测新方法分析.机械强度,2009,31(5):736-739
    [65] Yang J N, Lei Y. Identification of natural frequencies and damping ratios of linear structures via Hilbert transform and empirical mode decomposition, Proc. of International Conference on Intelligent Systems and control, IASTED/Acta press, Anaheim, CA, 1999:310~315.
    [66] Yang J N, Lei Y. Identification of tall building using nosy wind vibration data, Proc. of the International Conference on Advances in Structure Dynamics, Hong Kong,2000,2:1093~1100
    [67] Yang, J N, Lei Y, Pan S, Huang N. System identification of linear structures based on Hilbert Huang spectral analysis. Part 1: Normal modes[ J ]. EESD, 2003, 32: 1443~1467.
    [68]黄天立,楼梦麟.基于HHT的非线性结构系统识别研究.地震工程与工程振动,2006,26(3):80-83
    [69]陈隽,徐幼麟. HHT方法在结构模态参数识别中的应用.振动工程学报,2003,16(3):383-388
    [70]陈隽,徐幼麟,李杰. Hilbert-Huang变换在密频结构阻尼识别中的应用[ J ].地震工程与工程振动, 2003, 23 (4) : 34~42.
    [71]李传习,陈富强.基于HHT的结构损伤特征量与异常诊断.长沙理工大学学报(自然科学版),2007,4(3):29-33
    [72] David E. Rumelhart, James L. McClelland. Parallel distributed processing: explorations in the microstructure of cognition. vol. 2, Pages: 611 MIT PRESS 1986
    [73] Venkatasubramanian V and Chan K. A neural network methodology forprocess fault diagnosis. Journal of AICHE,1989,35(12):1993-2002
    [74] Wu X,Ghaboussi J and Garrett J H. Use of neural networks in detection of structural damage. Computer Structures. 1992,42(4):649-659
    [75] Masri. S. F., Nakamura, M., Chassiakos. A. G., et al. Neural network approach to detection of changes in structural parameters. Journal of Engineering Mechanics, 1996, 122:350-360
    [76]姜绍飞,刘明,倪一清,高赞明.大跨悬索桥损伤定位的自适应概率神经网络研究.土木工程学报,2003,36(8):74-78
    [77]吴波,胡云霞.基于BP神经网络的空间索杆结构节点损伤识别研究.地震工程与工程振动,2006,26(1)83-88
    [78]李宏男,高东伟,伊廷华.土木工程结构健康监测系统的研究状况与进展.力学进展,2008,38(2):151-166
    [79]邹大力,基于计算智能的结构损伤识别研究.大连理工大学博士学位论文,2005.
    [80]程远胜,区达光,谭国焕,白植洲.基于分级遗传算法的结构损伤识别方法.华中科技大学学报(自然科学版),2002,30(8):73-75
    [81]田东平,迟洪钦.混合遗传算法与模拟退火法[J ].计算机工程与应用, 2006, (22) : 63—65.
    [82] Wang L, Zheng D Z. An effective hybrid optimization strategy for job—shop scheduling problems [ J ]. Computers and Operations Research, 2001, ( 28 ) :585—596.
    [83]李守巨,刘迎曦,冯颖.基于混合遗传算法的动力系统阻尼参数识别方法[J ].计算力学学报, 2004, 21(5) : 551—556.
    [84]张茂雨.支持向量机方法在结构损伤识别中的应用.同济大学博士学位论文. 2007.
    [85] V. N. Vapnik, A. Ja. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Doklady A kademii Nauk USSR,1968, 181 (4 ) ( English Translation: Sov. Math. Dokl.)
    [86] V. N. Vapnik. The Nature of Statistical Learning Theory. Springer, Berlin,1995
    [87] Alex J. Smola, Bernhard Schoelkopf. A Tutorial on Support Vector Regression. Neuro-COLT2 Technical Report Series NC2-TR-1998030, October, 1998
    [88] Burge. CJC. A Tutorial on Support Vector Machines for Pattern Recognition [J]. Data Mining and Knowledge Discovery2, 1998: 121-167
    [89]樊可清,倪一清,高赞明.基于频域系统识别和支持向量机的桥梁状态监测方法.工程力学,2004,21(5):25-30
    [90]何浩祥,闫维明,周锡元.小波支持向量机在结构损伤识别中的应用研究.振动、测试与诊断,2007,27(1),53-57
    [91]郭惠勇,李正良,彭川.结构损伤动力识别技术的研究与进展.重庆建筑大学学报,2008,30(1):140-145
    [92]戴国莹.建筑结构基于性能要求的抗震措施初探.建筑结构,2010(10)
    [93] Loland K E. Concrete Damage Model for Load-Response Estimation of Concrete [J]. Cement and Concrete Research. 1980, 10: 395~402
    [94] Lee J., Fenves G L.. Plastic-damage model for cyclic loading of concrete structures [J]. Journal of Engineering Mechanics,1998, 124(8): 892~900
    [95] Lubliner J, Oliver J, Oller S, et al. A plastic-damage model for concrete [J]. International Journal of Solids and Structures. 1989, 25(3): 299~326
    [96] Légeron F, Paultre P. Uniaxial confinement model for normal and high-strength concrete columns [J]. Journal of Structural. Engineering., ASCE, 2005, 129(2): 241~252
    [97]王立明,顾祥林,沈祖炎,易天倚,孙飞飞.钢筋混凝土结构的损伤累积模型.工程力学增刊, 1997: 44~49
    [98] Hajrudin Pasic. A Unified Approach of Fracture and Damage Mechanics to Fatigue Damage Problems. International Journal of Solids and Structure, 2001, 1(29): 14~15
    [99]钱稼茹,程丽荣,周栋梁.普通箍筋约束混凝土柱的中心受压性能[J].清华大学学报, 2002, 42(10): 1369~1373
    [100]过镇海.混凝土的强度和本构关系—原理与应用[M].北京:中国建筑工业出版社, 2004
    [101] Saiidi M, Sozen M A. Simple Nonlinear Seismic Analysis of RC Structure [J]. ASCE, 1981, 107(5): 937~941
    [102] Bannon H, Biggs J M. Seismic Damage in Reinforced Concrete Frames [J]. Structure Engineering, ASCE, 1981, 107(9)
    [103] Roufaiel M S L, Meyer C. Analytical modeling of Hysteretic Behavior of RC Frames [J]. Journal of Structural Engineering ASCE, 1987, 113(3): 429~444
    [104] Powell G H, Allahabadi R. Seismic Damage Prediction by Deterministic Methods: Concepts and Procedures [J]. Earthquake Engineering and Structural Dynamics. 1988, 16: 719~734
    [105]王全凤,刘良林,沈章春.弹性变形能形式的地震损伤评价模型[J].建筑科学与工程学报. 2008, 25(4): 31~35
    [106] Young-Ji Park, Alfredo H S Ang. Mechanistic Seismic damage model for reinforced concrete [J]. Journal of Structural Engineering, ASCE, 1985, 111(4): 722~739
    [107] Young-Ji Park, Alfredo H S Ang, Weny K. Seismic damage analysis of reinforced concrete buildings [J]. Journal of Structural Engineering, 1985, 10( 4): 740~756
    [108] Kunnath S K, Reinhorn A M and Park Y J. Analytical Modeling of Inelastic Seismic Response of R—C Structures [J] . Journal of Structural Engineering , 1990 , 116(4) : 996~1017
    [109]江近仁,孙景江.砖结构的地震破坏模型.地震工程与工程振动, 1987(7)
    [110]欧进萍,牛荻涛,王光远.多层非线性抗震钢结构的模糊动力可靠性分析与设计.地震工程与工程振动, 1990(10)
    [111]牛荻涛,任利杰.改进的钢筋混凝土结构双参数地震破坏模型[J].地震工程与工程振动, 1996, 16(4): 44~54
    [112]王东升,冯启民,王国新.考虑低周疲劳寿命的改进Park-Ang地震损伤模型.土木工程学报, 2004,37(11): 41~49
    [113] Amador Teran, James O. Jirsa. A single low cycle fatigue model and its implication for seismic design [C]. 13th World Conference on Earthquake Engineering, 2004
    [114] Amador Teran, James O. Jirsa. The use of cumulative ductility strength spectra for seismic design against low cycle fatigue [C]. 13th World Conference on Earthquake Engineering, 2004
    [115]傅剑平,王敏,白绍良.对用于钢筋混凝土结构的Park-Ang双参数破坏准则的识别和修正.地震工程与工程振动, 2005, 25(5): 74~79
    [116]李洪泉,吴波,欧进萍.结构地震损伤后的抗震能力评估与试验.南京工业大学学报, 2002, 24(1): 62~66
    [117]吴波.主余震作用下钢筋混凝结构的损伤分析[D].哈尔滨:哈尔滨建筑大学, 1993
    [118]李洪泉,欧进萍.钢筋混凝土结构地震损伤识别方法[J].哈尔滨建筑大学学报, 1996(2): 9~12
    [119]王建民,李辉,陈龙珠.框架结构层间相对位移变化量在结构损伤检测中的应用[J].工业建筑, 2005, 35(11)
    [120]刘建伟,李洪泉.钢筋混凝土框架结构在三维地震作用下的累积损伤分析[D].北京:北京工业大学,2008
    [121]王丰,白海峰.钢混结构基于Park-Ang损伤准则的抗震设计研究[J].铁道建筑, 2008, (6): 108~110
    [122]王丰,李宏男,伊廷华.钢筋混凝土结构直接基于损伤性能目标的抗震设计方法[J].振动与冲击, 2009, 28(2)
    [123] Fajfar P. Equivalent ductility factors, taking into account low-cycle fatigue [J].Earthquake Engineering and Structural Dynamics. 1992, 21: 837~848
    [124] Fajfar P, Vidic T. Consistent inelastic design spectra: Hysteretic and input energy [J]. Earthquake Engineering and Structural Dynamics. 1994, 23: 523~537
    [125]刘海卿,陈小波,王学庆,王锦力.基于损伤指数的框架结构损伤演化研究[J].自然灾害学报, 2008,17(3): 29~35
    [126] Sozen M A. Review of earthquake response of reinforced concrete buildings with a view to drift control[C]. 7th World Conference on Earthquake Engineering, 1980
    [127] E. Stephens, J. T. P. Yao. Damage Assessment Using Response Measurements [J]. Journal of Structural Engineering, ASCE, 1987, 113(4): 787~801
    [128] Ghobarah A, Abou-elfath H, Biddah A. Response-based damage assessment of structures [J]. Earthquake Engineering and Structural Dynamics, 1999, 28(1): 79~104
    [129]朱红武,王孔藩,唐寿高.模态损伤指标及其在结构损伤评估中的应用[J].同济大学学报:自然科学版, 2004, 32(12): 1589
    [130] Ren W X, Guido D R. Structural damage identification using modal dataⅠ: simulation verification [J]. Journal of Structural Engineering, 2002, 128(1): 87
    [131] Dipasquale E, Cakmak AS. On the relation between local and global damage indices [R]. New York: National Center for Earthquake Engineering Research, 1989
    [132]李洪泉,欧进萍.剪切型钢筋混凝土结构的地震损伤识别方法[J] .哈尔滨建筑大学学报, 1996, 29(2): 8
    [133]张永利,基于HHT的混凝土结构地震损伤识别方法,南京工业大学2006年硕士论文
    [134]姚久纲,刘明才,李鸿晶,基于强震记录的建筑结构动力特性识别,低温建筑技术,2005年第5期,34-36
    [135]汪梦甫.基于振型损伤的高层建筑结构地震破坏准则[J].工程抗震与加固改造, 2008, 30(6): 24~32
    [136]闫桂荣,段忠东,欧进萍,基于结构振动信息的损伤识别研究综述,地震工程与工程振动,2007,27(3):95-103
    [137] Sun Z.,Chang C.C. Structural damage asses-sment based on wavelet packet transform. J.Struct.Engrg, ASCE,2002,128(10):1354-1361
    [138]任伟新,韩建刚,孙增寿,小波分析在土木工程结构中的应用,中国铁道出版社,2006年
    [139]秦寿康,综合评价原理与应用,电子工业出版社,2003年
    [140]卜一,吕西林等,采用增量动力分析方法确定高层混合结构的性能水准,结构工程师,2009,25(2):77-84
    [141]欧进萍,牛荻涛,王光远,非线性钢筋混凝土抗震结构的损失估计与优化设计.[J]土木工程学报,1993,26(5):5-7
    [142]李祚华.高层钢筋混凝土结构损伤模型及地震损伤描述[D].哈尔滨工业大学博士学位论文. 2009: 57~59
    [143]黄志华,吕西林,周颖,卜一.高层混合结构地震整体损伤指标研究[J].统计大学学报. 2010, 38(2): 170~177